Variational principle for frozen-in vortex structures interacting with sound waves

General properties of conservative hydrodynamic-type models are treated from positions of the canonical formalism adopted for liquid continuous media, with applications to the compressible Eulerian hydrodynamics, special- and general-relativistic fluid dynamics, and two-fluid plasma model including the Hall-magnetohydrodynamics. A variational formulation is found for motion and interaction of frozen-in localized vortex structures and acoustic waves in a special description where dynamical variables are, besides the Eulerian fields of the fluid density and the potential component of the canonical momentum, also the shapes of frozen-in lines of the generalized vorticity. This variational principle can serve as a basis for approximate dynamical models with reduced number of degrees of freedom.Comment: 7 pages, revtex4, no figure

The charged dust solution of Ruban -- matching to Reissner--Nordstr\"om and shell crossings

The maximally extended Reissner--Nordstr\"om (RN) manifold with $e^2 < m^2$ begs for attaching a material source to it that would preserve the infinite chain of asymptotically flat regions and evolve through the wormhole between the RN singularities. So far, the attempts were discouraging. Here we try one more possible source -- a solution found by Ruban in 1972 that is a charged generalisation of an inhomogeneous Kantowski--Sachs-type dust solution. It can be matched to the RN solution, and the matching surface must stay all the time between the two RN event horizons. However, shell crossings do not allow even half a cycle of oscillation between the maximal and the minimal size.Comment: journal reference adde

"Breathing" rogue wave observed in numerical experiment

Numerical simulations of the recently derived fully nonlinear equations of motion for weakly three-dimensional water waves [V.P. Ruban, Phys. Rev. E {\bf 71}, 055303(R) (2005)] with quasi-random initial conditions are reported, which show the spontaneous formation of a single extreme wave on the deep water. This rogue wave behaves in an oscillating manner and exists for a relatively long time (many wave periods) without significant change of its maximal amplitude.Comment: 6 pages, 12 figure

Atomic configuration and properties of austenitic steels at finite temperature: The effect of longitudinal spin fluctuations

High temperature atomic configurations of fcc Fe-Cr-Ni alloys with alloy composition close to austenitic steel are studied in statistical thermodynamic simulations with effective interactions obtained in ab initio calculations. The latter are done taking longitudinal spin fluctuations (LSF) into consideration within a quasiclassical phenomenological model. It is demonstrated that magnetic state affects greatly the alloy properties and in particular, it is shown that the LSF substantially modify the bonding and interatomic interactions of fcc Fe-Cr-Ni alloys even at ambient conditions. The calculated atomic short-range order (SRO) is in reasonable agreement with existing experimental data for Fe0.56}Cr0.21Ni0.23, which has strong preference for the (001) type ordering between Ni and Cr atoms. A similar ordering tendency is found for the Fe0.75Cr0.17Ni0.08 alloy composition, which approximately corresponds to the widely used 304 and 316 austenitic steel grades.Comment: 11 pages, 8 figures, 1 tabl